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Unveiling novel insights into Kirchhoff migration for effective object detection using experimental Fresnel dataset

Won-Kwang Park

Abstract

This study investigates the applicability of Kirchhoff migration (KM) for a fast identification of unknown objects in a real-world limited-aperture inverse scattering problem. To demonstrate the theoretical basis for the applicability including unique determination of objects, the imaging function of the KM was formulated using a uniformly convergent infinite series of Bessel functions of integer order of the first kind based on the integral equation formula for the scattered field. Numerical simulations performed using the experimental Fresnel dataset are exhibited to achieve the theoretical results.

Unveiling novel insights into Kirchhoff migration for effective object detection using experimental Fresnel dataset

Abstract

This study investigates the applicability of Kirchhoff migration (KM) for a fast identification of unknown objects in a real-world limited-aperture inverse scattering problem. To demonstrate the theoretical basis for the applicability including unique determination of objects, the imaging function of the KM was formulated using a uniformly convergent infinite series of Bessel functions of integer order of the first kind based on the integral equation formula for the scattered field. Numerical simulations performed using the experimental Fresnel dataset are exhibited to achieve the theoretical results.
Paper Structure (5 sections, 2 theorems, 18 equations, 3 figures)

This paper contains 5 sections, 2 theorems, 18 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Direct scattering problem and imaging function of the Kirchhoff migation
  3. Applicability of the Kirchhoff migration with experimental dataset
  4. Simulation results obtained using experimental data
  5. Conclusion

Key Result

Theorem 3.1

Let $\mathbf{x}-\mathbf{y}=|\mathbf{x}-\mathbf{y}|(\cos\phi,\sin\phi)$ and assume that $4k_{\mathrm{b}}|\mathbf{x}-\mathbf{r}_n|\gg1$ for all $n$ and $\mathbf{x}\in\Omega$. *Therefore, $\mathfrak{F}(\mathbf{x})$ can be expressed as follows: where $J_p$ denotes the Bessel function of order $p$.

Figures (3)

  • Figure 1: Illustration of generated MSR matrices.
  • Figure 2: Maps of $\mathfrak{F}(\mathbf{x})$ at $f=1,2,\ldots,8GHz$.
  • Figure 3: Maps of $\mathfrak{F}(\mathbf{x})$ at $f=1,2,\ldots,8GHz$.

Theorems & Definitions (3)

  • Theorem 3.1
  • proof
  • Corollary 3.1: Unique determination